Qhov khoom sib tshuam ntawm ob lub vectors, piv txwv li vectors A thiab B, yog sau ua A x B ( A hla B ). Cov khoom sib tshuam hu ua vector khoom vim tias qhov tshwm sim ntawm qhov kev sib ntxiv no tsim cov vector ntau.
Piv txwv li, vector A thiab vector B zoo li daim duab hauv qab no.
Txhawm rau txhais cov khoom sib tshuam ntawm cov vectors A dan B (A x B), peb kos lub vector A dan B raws li tau pom hauv daim duab saum toj no, thiab kuj tau piav qhia cov khoom sib xyaw vector B yog perpendicular rau A, uas yog sib npaug rau B sin theta.
Yog li, peb tuaj yeem txhais qhov loj ntawm cov khoom sib tshuam ntawm cov vectors. A dan B (A x B) ua cov khoom ntawm qhov loj ntawm lub vector A nrog cov khoom vector B perpendicular rau lub vector A.
Yog tias peb tig A x B mus ua B x A ces yuav ua li cas?
Ua ntej, peb kos cov vectors B thiab A thiab cov khoom ntawm vector A uas yog perpendicular rau B
Raws li daim duab no, peb tuaj yeem txhais cov khoom sib tshuam ntawm cov vectors B dan A (B x A) ua cov khoom ntawm qhov loj ntawm lub vector B nrog cov khoom vector A perpendicular rau lub vector B. Sau ua lej:
Kev Taw Qhia ntawm Kev Sib Npaug hla A x B
Cov khoom sib tshuam yog cov khoom vector, yog li qhov tshwm sim muaj ob qho tib si qhov loj thiab kev coj. Qhov loj ntawm cov khoom vector tau muab los saum toj no; tam sim no peb yuav tsum txiav txim siab nws qhov kev coj. Txhawm rau txiav txim siab qhov kev coj ntawm A x B , peb xub kos cov vectors A thiab B raws li qhia hauv qab no. Peb muab ob lub vectors no rau ntawm ib lub dav hlau.
Kev sib npaug ntawm kev sib npaug A x B yog txhais tias yog ib qho vector perpendicular rau lub dav hlau uas lub vector A dan B nyob. Qhov loj me zoo ib yam li AB kev txhaum tus phaujYog tias C = A x B maka C = AB kev txhaum tus phauj
Qhov kev taw qhia ntawm C yog perpendicular rau lub dav hlau uas cov vectors A thiab B pw. Peb tuaj yeem siv txoj cai sab tes xis los txiav txim siab qhov kev taw qhia ntawm C. Yog tias peb tuav peb cov ntiv tes rau hauv qhov kev taw qhia counterclockwise, ces qhov kev taw qhia ntawm C yog nyob rau hauv tib qho kev taw qhia li tus ntiv tes xoo taw rau saum toj.
Kev Taw Qhia ntawm Kev Sib Npaug hla B x A
Yuav kom paub qhov kev taw qhia B x A , ua ntej peb kos cov vectors B thiab A raws li qhia hauv qab no. Peb muab ob lub vectors no tso rau hauv ib lub dav hlau.
Yog tias C = B x A maka C = BA sin teta.
Qhov kev taw qhia ntawm C yog perpendicular rau lub dav hlau uas cov vectors B thiab A pw. Peb tuaj yeem siv txoj cai sab tes xis los txiav txim siab qhov kev taw qhia ntawm C. Yog tias peb tuav peb cov ntiv tes rau hauv qhov kev taw qhia clockwise, ces qhov kev taw qhia ntawm C yog tib yam li qhov kev taw qhia ntawm tus ntiv tes xoo taw rau hauv qab.
A x B tsis sib npaug rau B x A. Cov khoom sib tshuam ua rau muaj qhov ntau ntawm vector, uas tsis yog muaj qhov loj xwb, kuj muaj kev taw qhia. Hauv qhov poob saum toj no, kev taw qhia A x B kev taw qhia rov qab mus rau B x A.
Qee yam hais txog kev sib npaug ntawm cov lej uas koj yuav tsum paub:
1. Kev sib tshooj hla yog qhov tsis sib hloov pauv.
A x B = – B x A
Lub cim tsis zoo qhia tias qhov kev taw qhia ntawm B ntawm A x B yog qhov sib txawv rau qhov kev taw qhia ntawm B ntawm B x A.
2. Yog tias ob lub vectors sib ncaj rau ib leeg , lub kaum sab xis uas tsim yog 90 o . Sin 90 o = 1. Yog li, qhov loj ntawm cov khoom sib tshuam ntawm vectors A thiab B yuav tshwm sim raws li nram no:
A x B = AB sin theta = AB sin 90 o = AB
B x A = BA sin theta = BA sin 90 o = BA
3. Yog tias ob lub vectors nyob rau tib qho kev taw qhia, ces lub kaum sab xis tsim yog 0 o.
Sin 0 o = 0. Yog li, tus nqi ntawm cov khoom sib tshuam ntawm cov vectors A thiab B yuav tshwm sim raws li hauv qab no.
A x B = AB sin theta = AB sin 0 o = 0
B x A = BA sin theta = BA sin 0 o = 0
